1. Field of the Invention
The present invention relates to a method for determining the presence of transmitter sources and, as the case may be, their number in a system comprising at least one receiver receiving signals coming from radiocommunications transmitters.
It can be applied especially in the field of antenna processing where a system consisting of several antennas receives signals coming from radiocommunications transmitters. The signals sent are, for example, digital modulations comprising one or more synchronization signals.
It can also be applied in the field of the direction-finding or estimation of the angles of arrival of signals from RF sources, in order to obtain the values of incidence either of mobile sources or of base stations.
The detection of the number of sources present makes it possible especially to implement methods of high-resolution direction-finding.
The invention also relates to the field of adaptive filtering and of equalization for telecommunications. In particular, it relates to the techniques of synchronization with known reference sequences such as the TSC (Training Sequence Channel) or SCH (Synchronization Channel) sequences used in the GSM standard. These synchronization techniques make use of notions of detection.
2. Description of the Prior Art
There are known, prior art ways of estimating the number M0 of sources in a radiocommunications system.
For example, a standard estimation method consists of the application of a MUSIC type algorithm, known to those skilled in the art. For this purpose, it is necessary to know the number of incident sources which is equal to the rank of the covariance matrix Rxx=E[x(t)x(t)H] of the signals x(t) received by the sensors. The rank of the covariance matrix of the sensor signals x(t) is determined from an estimate of this matrix on T statistically independent samples x(tk):                                           R            ^                    xx                =                              1            T                    ⁢                                    ∑                              k                =                1                            T                        ⁢                                                            x                  _                                ⁡                                  (                                      t                    k                                    )                                            ⁢                                                                    x                    _                                    ⁡                                      (                                          t                      k                                        )                                                  H                                                                        (        1        )            such that                     x        _            ⁡              (        t        )              =                            ∑                      m            =            1                                M            0                          ⁢                                            a              _                        ⁡                          (                              u                m                            )                                ⁢                                    s              m              0                        ⁡                          (              t              )                                          +                        b          _                ⁡                  (          t          )                      ,with b(t) being the Gaussian white noise, m the index of the transmitter or the transmitter source, a(um) the direction vector of the incidence source um and sm0(t) the signal transmitted by this mth source. A source may be a multipath source coming from the transmitter.
In the presence of M0 sources with a Gaussian time signal x(tk), the likelihood ratio, Vclassic(M=M0/M0), using the N−M0 lowest eigenvalues of the matrix {circumflex over (R)}xx, follows a chi-2 relationship with (N−M0)2−1 degrees of freedom, given that:                                                         V              classic                        ⁡                          (                              M                /                                  M                  0                                            )                                =                                    -              2                        ⁢                          T              ⁡                              [                                                      ln                    ⁡                                          (                                              [                                                                              ∏                                                          m                              =                                                              M                                +                                1                                                                                      N                                                    ⁢                                                      λ                            m                                                                          ]                                            )                                                        -                                                            (                                              N                        -                        M                                            )                                        ⁢                                          ln                      ⁡                                              (                                                                              σ                            ^                                                    2                                                )                                                                                            ]                                                    ⁢                                  ⁢                              with            ⁢                                                   ⁢                                          σ                ^                            2                                =                                    1                              N                -                M                                      ⁢                                          ∑                                  m                  =                                                            M                      0                                        +                    1                                                  N                            ⁢                              λ                m                                                                        (        2        )                λm: eigenvalue of {circumflex over (R)}xx for 1≦m≦N    N: number of sensors of the reception system or number of reception channels.This gives a likelihood law:Vclassic([M=M0]/M0)˜Chi-2 at (N−M0)2−1 with dim{x(t)}=N  (3)
Knowledge of the law of probability of Vclassic(M0/M0) makes it possible to fix the threshold αM for which the probability of having a number of sources strictly greater than M sources is close to 1 (pd˜1): the thresholds αM are chosen in the chi-2 table with a low probability of false alarms pfa and a number of degrees of freedom equal to (N−M)2−1. With the law of probability Vclassic(M0/M0) being known, it is sought to take the maximum value of the random variable Vclassic(M0/M0) so that Vclassic(M0/M0)<αM with a probability of 1−pfa. It is then possible to construct the following detection test:    if Vclassic(M/M0)≧αM, the number of sources M0 present is greater than M,    if Vclassic(M/M0)<αM, the number of sources M0 present is smaller than or equal to M.
To determine the number of sources M0, first the presence of M=0 sources is tested, then that of M=1 until Vclassic(M/M0) is lower than the threshold αM. The number of sources then corresponds to the value verifying the inequality: if Vclassic(M/M0)<αM then M0=M is taken. It is recalled that this statistical detection test can work only when the noise b(t) is white, namely when its covariance matrix verifies:Rbb=E[b(t)b(t)H]=σ2Iwhere I is the N×N-sized unit matrix.
There is also a known prior art method for estimating the number M0 of sources common to two observations u(t) and v(t) of a same length.
In this case, it is necessary to know the rank of an intercorrelation matrix Ruv=E[u(t)v(t)H] between observations u(t) and v(t) recorded on an array of N sensors capable of performing reference direction-finding algorithms. Indeed, a reference sequence of a mobile may appear at the instants t0 and t0+Tframe where Tframe designates the length of a GSM frame, for example. In these conditions, it is possible to build an intercorrelation matrix Ruv with non-zero energy from the signals u(t)=x(t−t0) and v(t)=x(t−t0−Tframe).
In general, it is sought to determine the number M0 of sources common to the signals u(t) and v(t) such that:                                           u            _                    ⁡                      (            t            )                          =                                                            ∑                                  m                  =                  1                                                  M                  0                                            ⁢                                                                    a                    _                                    ⁡                                      (                                          u                      m                                        )                                                  ⁢                                                      s                    m                    0                                    ⁡                                      (                    t                    )                                                                        +                                                                                b                    _                                    u                                ⁡                                  (                  t                  )                                            ⁢                                                           ⁢              and              ⁢                                                           ⁢                                                v                  _                                ⁡                                  (                  t                  )                                                              =                                                    ∑                                  m                  =                  1                                                  M                  0                                            ⁢                                                                    a                    _                                    ⁡                                      (                                          u                      m                                        )                                                  ⁢                                                      s                    m                    0                                    ⁡                                      (                    t                    )                                                                        +                                                            b                  _                                v                            ⁡                              (                t                )                                                                        (        4        )            
The observations u(t) and v(t) are distinguished by the noise vectors bu(t) and bv(t) constituted by background noise as well as interferers received independently on u(t) and v(t). The vectors bu(t) and bv(t) are statistically decorrelated and Gaussian. The method determines the rank of the matrix Ruv from an estimate of this matrix on T samples u(tk) and then v(tk) that are statistically independent:                                           R            ^                    uv                =                              1            T                    ⁢                                    ∑                              k                =                1                            T                        ⁢                                                            u                  _                                ⁡                                  (                                      t                    k                                    )                                            ⁢                                                                    v                    _                                    ⁡                                      (                                          t                      k                                        )                                                  H                                                                        (        5        )            
To know the rank of the matrix {circumflex over (R)}uv, the rank of its standardized form R is estimated. In the presence of M0 sources with Gaussian time signals u(tk) and v(tk), the likelihood ratio Vuv(M=M0/M0) using the N−M0lowest eigenvalues of R follows a chi-2 relationship with 2(N−M0)2 degrees of freedom. This likelihood ratio verifies:                                           V            uv                    ⁡                      (                          M              /                              M                0                                      )                          =                              -            2                    ⁢          T          ⁢                                           ⁢                      ln            ⁡                          (                              [                                                      ∏                                          m                      =                                              M                        +                        1                                                              N                                    ⁢                                      μ                    m                                                  ]                            )                                                          (        6        )            where μm is an eigenvalue of R=I-UUH classified in descending order for 1≦m≦N, N being the number of sensors. The matrix U is built from vectors u(tk) and v(tk) as follows:U={circumflex over (R)}uu−1/2{circumflex over (R)}uv{circumflex over (R)}vv−1/2 such that:            R      ^        uu    =                    1        T            ⁢                        ∑                      k            =            1                    T                ⁢                                            u              _                        ⁡                          (                              t                k                            )                                ⁢                                                    u                _                            ⁡                              (                                  t                  k                                )                                      H                    ⁢                                           ⁢          and          ⁢                                           ⁢                                    R              ^                        vv                                =                  1        T            ⁢                        ∑                      k            =            1                    T                ⁢                                            v              _                        ⁡                          (                              t                k                            )                                ⁢                                                    v                _                            ⁡                              (                                  t                  k                                )                                      H                              The likelihood relationship is then expressed as follows (7):    Vuv(M=M0/M0)˜Chi-2 with 2(N−M0)2 degrees of freedom with dim{u(t)}=dim{v(t)}=N×1
Knowledge of the law of probability of Vuv(M0/M0) makes it possible to fix the threshold αM for which the probability of having a number of sources strictly greater than M sources is close to 1 (pd˜1): the thresholds αM are chosen in the chi-2 table with a low probability of false alarms pfa and a number of degrees of freedom equal to 2(N−M)2. With the law of probability Vuv(M0/M0) being known, it is sought to take the maximum value of the random variable Vuv(M0/M0) so that Vuv(M0/M0)<αM with a probability of 1−pfa. It is then possible to construct the following detection test:    if Vuv(M/M0)>αM, the number of sources M0 present is greater than M,    if Vuv(M/M0)<αM, the number of sources M0 present is smaller than or equal to M.
To determine the number of sources M0, first the presence of M=0 sources is tested, then that of M=1 until Vuv(M/M0) is lower than the threshold αM. The number of sources then corresponds to the value verifying the inequality: if Vuv(M/M0)<αM then M0=M is taken.
While the methods described in the prior art give good results in certain cases, they are nevertheless limited in their application. For example, they cannot be used to detect the presence and/or number of sources common to several observations u(t) and v(t) having different lengths.